Question

Given: A nutrition store in the mall is selling “Memory Booster” which is a concoction of herbs and minerals that is intended to improve memory performance. To test the hypothesized memory enhancement of the herbal mix, the now famous drug researcher, Dr. Mindfog, obtains a sample of 15 adult volunteers and has each person take the suggested dosage each day for 4 weeks. At the end of the four-week period, each individual takes a standardized memory test. In the general adult population, the standardized memory test is known to have a mean of italic mu = 10, where higher scores demonstrate better performance on the test of memory. The scores for the 15 volunteers are: 12, 11, 13, 15, 8, 11, 13, 15, 10, 9, 10, 16, 15, 11, 14 Which hypothesis test needs to be employed here?

Group of answer choices

z test

one-sample t test

dependent t test

independent t test

Pearson's r

Answer 1

Solution:

Answer is

one-sample t test

Explanation:

Claim is " standardized memory test is known to have a mean of italic mu = 10 "

i.e = 10

where is the population mean .

So the null and alternative hypothesis can be written as

H₀ : = 10 vs H₁ :    10

We have a sample of size n = 15

12, 11, 13, 15, 8, 11, 13, 15, 10, 9, 10, 16, 15, 11, 14

We need to perform one sample test for the mean.

There are two ways for this.

1)One sample z test for mean - if population standard deviation is known

2)One sample t test for mean - if the population standard deviation is unknown.

Here , the population standard deviation is unknown. In this case we use sample standard deviation s and perform t test.

So , answer is

one-sample t test.